# ITSY: Causal Discovery From Irregular Time-Series Data

arXiv: https://arxiv.org/abs/2609.23516 · HTML: https://mlsanity.com/paper/2609.23516/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 46 references that are in the map.
- First posted on arXiv 20 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Causal Recurrent Variational Autoencoder for Medical Time Series Generation](https://mlsanity.com/paper/2301.06574/) (2023)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge](https://mlsanity.com/paper/2109.04286/) (2021)
- [CUTS: Neural Causal Discovery from Irregular Time-Series Data](https://mlsanity.com/paper/2302.07458/) (2023)
- [Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise](https://mlsanity.com/paper/2210.14706/) (2022)
- [Reconstructing regime-dependent causal relationships from observational time series](https://mlsanity.com/paper/2007.00267/) (2020)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [Neural Structure Learning with Stochastic Differential Equations](https://mlsanity.com/paper/2311.03309/) (2023)
- [Causal Discovery from Subsampled Time Series with Proxy Variables](https://mlsanity.com/paper/2305.05276/) (2023)
- [Causal Discovery from Time Series with Hybrids of Constraint-Based and Noise-Based Algorithms](https://mlsanity.com/paper/2306.08765/) (2023)
- [Causal Discovery for Irregularly Time Series with Consistency Guarantees](https://mlsanity.com/paper/2507.03310/) (2025)
- [Causal Structure Learning for Dynamical Systems with Theoretical Score Analysis](https://mlsanity.com/paper/2512.14361/) (2025)

## Abstract (arXiv)

Structural causal models for time series recover contemporaneous and lagged effects, but most methods require complete observation windows and become misspecified when samples are missing. We introduce ITSY, the first continuous-optimization method for causal discovery from irregular time series under a linear model. ITSY reformulates the structural equation so that prediction uses the nearest available history rather than the possibly missing current slice, and jointly imputes missing values while learning both graphs. A weighted reconstruction objective corrects the noise transformation induced by this reformulation. Across synthetic regimes varying missingness, scale, graph density, and noise, and on a real world benchmark, ITSY consistently improves graph recovery over representative SCM-based baselines, demonstrating the effectiveness of the proposed method. The results establish a focused solution for irregular linear first-order dynamics and clarify the assumptions required for nonlinear or higher-order extensions.